What is Mediation?

• Refers to a situation when the relationship between a predictor variable and outcome variable can be explained by their relationship to a third variable (the mediator).

Baron & Kenny (1986)

• Mediation is tested through three regression models:

  • Predicting the outcome from the predictor variable.
  • Predicting the mediator from the predictor variable.
  • Predicting the outcome from both the predictor variable and the mediator.

Baron & Kenny (1986)

• Four conditions of mediation:

  • The predictor must significantly predict the outcome variable.*
  • The predictor must significantly predict the mediator.
  • The mediator must significantly predict the outcome variable.
  • The predictor variable must predict the outcome variable less strongly in model 3 than in model 1.

Baron & Kenny (1986): Limitations

• How much of a reduction in the relationship between the predictor and outcome is necessary to infer mediation?

• People tend to look for a change in significance, which can lead to the ‘all or nothing’ thinking that p-values encourage.

• Two solutions:

  • The Sobel test
  • Bootstrapping the indirect effect and confidence intervals

Sobel Test

• An alternative is to estimate the indirect effect and its significance using the Sobel test (Sobel, 1982).
• If the Sobel test is significant, there is significant mediation
• We are going to use the Aroian Test version of Sobel which corrects for the standard error of the a and b paths.

Bootstrapping

• What is bootstrapping?

  • A procedure where you run an analysis many times to create an average effect and confidence interval of the effect.
  • Bootstrapped datasets are created by randomly picking a sample from your dataset with replacement
  • Think about this like the lottery, if they put the balls back.
  • If the confidence interval of the indirect (mediation) effect does not cross zero, then that implies that mediation has occurred.

Mediation: Data Screening

• Mediation models usually occur in stages - meaning separate models are run with different IV / DV combinations.

• Sometimes people call these “steps”, but do not confuse this with hierarchical regression.

• So, what does that do for data screening?

  • Screen both the IV and the Mediator at the same time predicting the DV.
  • This way you are screening the final anticipated stage of the mediation model and are screening all the variables.
  • You can also use the fake regression procedure to do all three variables at once.

Mediation: Example

• Does Facebook use mediate the relationship between previous knowledge and exam scores?
• Implying that the overuse of Facebook prevents people from studying, so they do differently on their exam?
• Important not to have missing data, so you are comparing models that all use the same data points.

library(rio)
master <- import("data/mediation.sav")
str(master)

## 'data.frame':    240 obs. of  3 variables:
##  $ previous: num  3 2 1 1 1 1 1 1 1 1 ...
##   ..- attr(*, "format.spss")= chr "F1.0"
##   ..- attr(*, "display_width")= int 14
##  $ facebook: num  3.67 5 4 4.5 4.5 ...
##   ..- attr(*, "format.spss")= chr "F8.2"
##   ..- attr(*, "display_width")= int 14
##  $ exam    : num  1 1 2 7 6 1 2 1 1 1 ...
##   ..- attr(*, "format.spss")= chr "F8.2"
##   ..- attr(*, "display_width")= int 10

summary(master)

##     previous        facebook          exam       
##  Min.   :1.000   Min.   :1.750   Min.   : 1.000  
##  1st Qu.:1.000   1st Qu.:3.750   1st Qu.: 1.000  
##  Median :1.000   Median :4.250   Median : 1.000  
##  Mean   :1.571   Mean   :4.143   Mean   : 1.825  
##  3rd Qu.:2.000   3rd Qu.:4.750   3rd Qu.: 2.000  
##  Max.   :7.000   Max.   :5.000   Max.   :11.000  
##                  NA's   :1

master <- na.omit(master)

Mediation: c Path

• The c path: X –> Y: \[b = 0.32, t(237) = 3.63, p < .001\]

model1 <- lm(exam ~ previous, data = master)
summary(model1)

## 
## Call:
## lm(formula = exam ~ previous, data = master)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9092 -0.6477 -0.6477  0.3523  8.4062 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.33228    0.16749   7.955 7.37e-14 ***
## previous     0.31539    0.08689   3.630 0.000348 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.496 on 237 degrees of freedom
## Multiple R-squared:  0.05266,    Adjusted R-squared:  0.04867 
## F-statistic: 13.17 on 1 and 237 DF,  p-value: 0.0003476

Mediation: a Path

• The a path: X –> M: \[b = -0.09, t(237) = -2.17, p = .031\]

model2 <- lm(facebook ~ previous, data = master)
summary(model2)

## 
## Call:
## lm(formula = facebook ~ previous, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.44609 -0.44609  0.05391  0.55391  1.35640 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.28817    0.08195  52.330   <2e-16 ***
## previous    -0.09208    0.04251  -2.166   0.0313 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.732 on 237 degrees of freedom
## Multiple R-squared:  0.01941,    Adjusted R-squared:  0.01527 
## F-statistic: 4.692 on 1 and 237 DF,  p-value: 0.03131

Mediation: b, c’ Path

• Add in the b and c’ paths: X + M –> Y
• b Path: \[b = -0.61, t(237) = -4.77, p < .001\]
• c’ Path: \[b = 0.26, t(237) = 3.09, p = .002\]

model3 <- lm(exam ~ previous + facebook, data = master)
summary(model3)

## 
## Call:
## lm(formula = exam ~ previous + facebook, data = master)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6065 -0.7666 -0.3117  0.3850  7.9999 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.93294    0.56791   6.925 4.09e-11 ***
## previous     0.25954    0.08397   3.091  0.00224 ** 
## facebook    -0.60647    0.12705  -4.773 3.18e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.432 on 236 degrees of freedom
## Multiple R-squared:  0.1361, Adjusted R-squared:  0.1288 
## F-statistic: 18.59 on 2 and 236 DF,  p-value: 3.194e-08

Mediation: Interpretation

• Previous experience positively impacts exam scores (c path = 0.32).
• Previous experience negatively impacts Facebook time (a path = -0.09).
• Controlling for previous experience, Facebook time negatively impacts exam scores (b path = -0.61).
• Controlling for Facebook scores, previous experience positively impacts exam scores (c’ path = 0.26).
• So, did mediation happen? Is a change from 0.31 to 0.26 important?

Mediation: Sobel Test

• The Aroian Test: \(Z = \frac{a \times b}{\sqrt{b^2 \times SD_a^2 + a^2 \times SD_b^2 + SD_a^2 \times SD_b^2}}\)

• If the indirect effect is larger than the error, we would conclude that the addition of the M variable changed the c path.

  • Fill in the correct coefficient numbers
  • Note if you use this code provided and fill in X and M in the correct order, you will not need to change the Sobel code.

#aroian sobel
a <- coef(model2)[2]
b <- coef(model3)[3]
SEa <- summary(model2)$coefficients[2,2]
SEb <- summary(model3)$coefficients[3,2]
zscore <- (a*b)/(sqrt((b^2*SEa^2)+(a^2*SEb^2)+(SEa^2*SEb^2)))
zscore

## previous 
## 1.937494

#two tailed test 
pnorm(abs(zscore), lower.tail = F)*2

##   previous 
## 0.05268497

Mediation: Sobel Test

• Z = 1.93, p = .053
• We would conclude that no mediation had occurred.

Mediation: All Together + Bootstrapping

#devtools::install_github("doomlab/MeMoBootR")
library(MeMoBootR)

## Loading required package: boot

## Loading required package: diagram

## Loading required package: shape

## Loading required package: ggplot2

#no missing data allowed
med_results <- mediation1(y = "exam",
                          x = "previous", 
                          m = "facebook", 
                          df = master)

Mediation: MeMoBootR

• The MeMoBootR package gives you data screening, each step of the mediation, and the bootstrapping results!
• The data screening does not include accuracy or missing data, so that should be completed first.

head(med_results$datascreening$fulldata)

##   previous facebook exam badmahal badleverage badcooks totalout
## 1        3 3.666667    1        0           0        0        0
## 2        2 5.000000    1        0           0        0        0
## 3        1 4.000000    2        0           0        0        0
## 4        1 4.500000    7        0           0        1        1
## 5        1 4.500000    6        0           0        1        1
## 6        1 4.500000    1        0           0        0        0

med_results$datascreening$correl

##             (Intercept)   previous   facebook
## (Intercept)   1.0000000 -0.3617623 -0.9593469
## previous     -0.3617623  1.0000000  0.1393247
## facebook     -0.9593469  0.1393247  1.0000000

med_results$datascreening$linearity

med_results$datascreening$normality

med_results$datascreening$homogen

Mediation: MeMoBootR

• For each of our stages of mediation, you can print out the models:

summary(med_results$model1)

## 
## Call:
## lm(formula = allformulas$eq1, data = finaldata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9092 -0.6477 -0.6477  0.3523  8.4062 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.33228    0.16749   7.955 7.37e-14 ***
## previous     0.31539    0.08689   3.630 0.000348 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.496 on 237 degrees of freedom
## Multiple R-squared:  0.05266,    Adjusted R-squared:  0.04867 
## F-statistic: 13.17 on 1 and 237 DF,  p-value: 0.0003476

summary(med_results$model2)

## 
## Call:
## lm(formula = allformulas$eq2, data = finaldata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.44609 -0.44609  0.05391  0.55391  1.35640 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.28817    0.08195  52.330   <2e-16 ***
## previous    -0.09208    0.04251  -2.166   0.0313 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.732 on 237 degrees of freedom
## Multiple R-squared:  0.01941,    Adjusted R-squared:  0.01527 
## F-statistic: 4.692 on 1 and 237 DF,  p-value: 0.03131

summary(med_results$model3)

## 
## Call:
## lm(formula = allformulas$eq3, data = finaldata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6065 -0.7666 -0.3117  0.3850  7.9999 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.93294    0.56791   6.925 4.09e-11 ***
## previous     0.25954    0.08397   3.091  0.00224 ** 
## facebook    -0.60647    0.12705  -4.773 3.18e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.432 on 236 degrees of freedom
## Multiple R-squared:  0.1361, Adjusted R-squared:  0.1288 
## F-statistic: 18.59 on 2 and 236 DF,  p-value: 3.194e-08

Mediation: MeMoBootR

• Next, you can get the Sobel test results:

med_results$indirect.effect

##   previous 
## 0.05584541

med_results$z.score

## previous 
## 1.937494

med_results$p.value

##   previous 
## 0.05268497

Mediation: MeMoBootR

• Last, let’s get the bootstrapped results:

  • The indirect effect would be reported as: \(0.06, 95\% CI[-0.01, 0.12]\)

med_results$boot.results

## 
## ORDINARY NONPARAMETRIC BOOTSTRAP
## 
## 
## Call:
## boot(data = finaldata, statistic = indirectmed, R = nboot, formula2 = allformulas$eq2, 
##     formula3 = allformulas$eq3, x = x, med.var = m)
## 
## 
## Bootstrap Statistics :
##       original     bias    std. error
## t1* 0.05584541 0.00102295  0.03210787

med_results$boot.ci

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = bootresults, conf = conf_level, type = "norm")
## 
## Intervals : 
## Level      Normal        
## 95%   (-0.0081,  0.1178 )  
## Calculations and Intervals on Original Scale

med_results$diagram

Moderation

• The combined effect of two variables on another is known conceptually as moderation, and in statistical terms as an interaction effect.

• Do violent video games make people aggressive?

  • DV: Aggression

  • IV:

    • Callous unemotional traits
    • Number of hours spent playing video games per week
    • Interaction

Conceptual Moderation Model

• If callous-unemotional traits were a moderator then we’re saying that the strength or direction of the relationship between game playing and aggression depends on the strength of callous-unemotional traits.

Conceptual Moderation Model

• If the X variable was categorical, you are basically checking if the separate groups (levels) have different slopes for the non-categorical variable.

Conceptual Moderation Model

• However, if X is continuous, we have to find a new way to figure out the shape of the interaction.

Statistical Moderation Model

Centering variables

• The interaction term makes the bs for the main predictors uninterpretable in many situations.

• Centering refers to the process of transforming a variable into deviations around a fixed point.

• Centering solves two problems:

  • Interpretation
  • Multicollinearity

Centering variables

• Easiest way to center to make them useful:

  • Score - Mean for that variable.
  • What does that do?

• Centered variables for main effects have two interpretations

  • Effect of that predictor at the mean value for the sample
  • Average effect of the predictor across a range of scores for the other predictor

Moderation: Simple Slopes

• If the interaction is significant, then you usually ignore the main effects (each variable by itself).
• So what do I do if my interaction is significant? A simple slope analysis
• If variables are categorical, then you are simply looking at the differences across one variable or another

Moderation: Simple Slopes

• For continuous variables, you “create” low, average, and high groups.

  • Low groups are people who are one SD below the mean
  • Average groups are people are at the mean
  • High groups are people who are one SD above the mean
  • However, creating groups is backwards from what you think.

Moderation: Simple Slopes

• We are examining the interaction between hours of video games and unemotional traits to predict aggression
• Think about which variable you want to know the differences in (i.e., low, average, high).
• So at different levels of callousness, we want to examine the relationship between hours of video games and aggression.

master <- import("data/moderation.sav")
str(master)

## 'data.frame':    442 obs. of  4 variables:
##  $ ID        : num  69 55 7 96 130 124 72 139 102 179 ...
##   ..- attr(*, "label")= chr "Case ID"
##   ..- attr(*, "format.spss")= chr "F3.0"
##  $ Aggression: num  13 38 30 23 25 46 41 22 35 23 ...
##   ..- attr(*, "label")= chr "Agression"
##   ..- attr(*, "format.spss")= chr "F2.0"
##  $ Vid_Games : num  16 12 32 10 11 29 23 15 20 20 ...
##   ..- attr(*, "label")= chr "Video Games (Hours per week)"
##   ..- attr(*, "format.spss")= chr "F2.0"
##  $ CaUnTs    : num  0 0 0 1 1 1 2 3 3 3 ...
##   ..- attr(*, "label")= chr "Callous Unemotional Traits"
##   ..- attr(*, "format.spss")= chr "F2.0"

Moderation: Centering

• Center your variables using scale()

  • Using scale = F turns off dividing by SD, which would create z-scores.
  • You can use z-score centering if you wanted the coefficients to be beta. It is likely easier to interpret the b values though.

#center the X and M variable (NOT THE DV)
#when you create these use the final dataset 
master$zvid = scale(master$Vid_Games, scale = F) #mean center, not z score
master$zcal = scale(master$CaUnTs, scale = F)

Moderation: Running

• For data screening, we would screen the model with the interaction, and all other considerations are the same as regression.

• Run the model:

  • You do not have to create an interaction column, to multiply does that automatically for you.
  • Also includes the main effects of each variable by itself.

#run the model to see if the moderation is significant
#use the z score variables!
#be sure to do X*M so the graph is right 
modmodel <- lm(Aggression ~ zvid*zcal, data = master)

Moderation: Interpretation

• Overall model is significant, \(F(3, 438) = 88.46, p < .001, R^2 = .38\)
• Interaction effect is significant, \(b = 0.03, t(438) = 3.88, p < .001\)

summary(modmodel)

## 
## Call:
## lm(formula = Aggression ~ zvid * zcal, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.967108   0.475057  84.131  < 2e-16 ***
## zvid         0.169625   0.068473   2.477 0.013616 *  
## zcal         0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcal    0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• So, how do we create groups when we have a continuous variable?

  • Most people look at “low” as one SD below the mean and “high” as one SD above the mean.
  • Lots of combinations are possible though.

Moderation: Simple Slopes

• Create the low and high versions of the M variable (callousness in this example)

  • Low created by ADDING a SD
  • High created by SUBTRACTING a SD
  • The rule is that we have to bring them to the middle because we centered so that zero is the middle

#create the low and high z score variables 
master$zcallow <- master$zcal + sd(master$zcal) #bring them up
master$zcalhigh <- master$zcal - sd(master$zcal) #bring them down
summary(master)

##        ID          Aggression      Vid_Games         CaUnTs    
##  Min.   :  1.0   Min.   : 9.00   Min.   : 1.00   Min.   : 0.0  
##  1st Qu.:111.2   1st Qu.:32.00   1st Qu.:17.00   1st Qu.:11.0  
##  Median :221.5   Median :40.00   Median :22.00   Median :18.0  
##  Mean   :221.5   Mean   :40.05   Mean   :21.84   Mean   :18.6  
##  3rd Qu.:331.8   3rd Qu.:48.00   3rd Qu.:26.00   3rd Qu.:26.0  
##  Max.   :442.0   Max.   :82.00   Max.   :38.00   Max.   :43.0  
##        zvid.V1              zcal.V1            zcallow.V1    
##  Min.   :-20.843891   Min.   :-18.595023   Min.   :-8.97733  
##  1st Qu.: -4.843891   1st Qu.: -7.595023   1st Qu.: 2.02267  
##  Median :  0.156109   Median : -0.595023   Median : 9.02267  
##  Mean   :  0.000000   Mean   :  0.000000   Mean   : 9.61769  
##  3rd Qu.:  4.156109   3rd Qu.:  7.404977   3rd Qu.:17.02267  
##  Max.   : 16.156109   Max.   : 24.404977   Max.   :34.02267  
##      zcalhigh.V1     
##  Min.   :-28.212716  
##  1st Qu.:-17.212716  
##  Median :-10.212716  
##  Mean   : -9.617693  
##  3rd Qu.: -2.212716  
##  Max.   : 14.787284

Moderation: Simple Slopes

• Then run the model with the new low and high versions of the variable.
• What do I do with that?
• You look at the other variable because the coefficients for M and X*M will not change.

#run the models
#be sure to X*M
modmodellow <- lm(Aggression ~ zvid*zcallow, data = master)
modmodelhigh <- lm(Aggression ~ zvid*zcalhigh, data = master)

Moderation: Simple Slopes

• At low levels of callousness, video game hours is unrelated to aggression, b = -0.09 …

summary(modmodellow) #low slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcallow, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  32.656771   0.672018  48.595  < 2e-16 ***
## zvid         -0.090651   0.099105  -0.915 0.360854    
## zcallow       0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcallow  0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• At average levels of callousness, hours of video games predicts increasing aggression, b = 0.17 …

summary(modmodel) #average slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcal, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.967108   0.475057  84.131  < 2e-16 ***
## zvid         0.169625   0.068473   2.477 0.013616 *  
## zcal         0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcal    0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• At high levels of callousness, the strength of hours of video games predicting aggression is the strongest, b = 0.43 …

summary(modmodelhigh) #high slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcalhigh, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   47.277446   0.672520  70.299  < 2e-16 ***
## zvid           0.429901   0.092577   4.644 4.53e-06 ***
## zcalhigh       0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcalhigh  0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• Significant interactions will create fan effects of slopes that either get stronger/weaker in strength or switch directions.
• Here, we find that increasing levels of callousness leads to increasing effects of video game time on aggression.

Moderation: Graphing

• We can use the ggplot to create a graph of the moderation effect.
• But we are going to manually draw the lines on a scatterplot graph.

library(ggplot2)
cleanup <- theme(panel.grid.major = element_blank(), 
                panel.grid.minor = element_blank(), 
                panel.background = element_blank(), 
                axis.line.x = element_line(color = "black"),
                axis.line.y = element_line(color = "black"),
                legend.key = element_rect(fill = "white"),
                text = element_text(size = 15))

modgraph <- ggplot(master, aes(zvid, Aggression))

##change Cal to the new moderator label
##change xlab for the new X label
modgraph + 
  xlab("Centered Video Games") + 
  geom_point(color = "gray") +
  geom_abline(aes(intercept = modmodellow$coefficients[1],
                  slope = modmodellow$coefficients[2], 
                  linetype = "-1SD Cal"), size = 1) +
  geom_abline(aes(intercept = modmodel$coefficients[1],
                  slope = modmodel$coefficients[2], 
                  linetype = "Average Cal"), size = 1) +
  geom_abline(aes(intercept = modmodelhigh$coefficients[1],
                  slope = modmodelhigh$coefficients[2], 
                  linetype = "+1SD Cal"), size = 1) +
  scale_linetype_manual(values = c("dotted", "dashed", "solid"),
                        breaks = c("-1SD Cal", "Average Cal", "+1SD Cal"),
                        name = "Simple Slope") +
  cleanup 

Moderation: MeMoBootR

• We can use the MeMoBootR to complete the entire processing, including data screening for us!
• You would enter the raw variables, as the centering is completed for you.

mod_model <- moderation1(y = "Aggression",
                         x = "Vid_Games",
                         m = "CaUnTs",
                         df = master)

Moderation: MeMoBootR

#data screening
head(mod_model$datascreening$fulldata)

##    ID Aggression Vid_Games CaUnTs       zvid      zcal  zcallow  zcalhigh
## 1  69         13        16      0  -5.843891 -18.59502 -8.97733 -28.21272
## 2  55         38        12      0  -9.843891 -18.59502 -8.97733 -28.21272
## 3   7         30        32      0  10.156109 -18.59502 -8.97733 -28.21272
## 4  96         23        10      1 -11.843891 -17.59502 -7.97733 -27.21272
## 5 130         25        11      1 -10.843891 -17.59502 -7.97733 -27.21272
## 6 124         46        29      1   7.156109 -17.59502 -7.97733 -27.21272
##   badmahal badleverage badcooks totalout
## 1        0           0        1        1
## 2        0           1        0        1
## 3        0           1        0        1
## 4        0           1        0        1
## 5        0           1        0        1
## 6        0           1        1        2

#mod_model$datascreening$correl
#mod_model$datascreening$linearity
#mod_model$datascreening$normality
#mod_model$datascreening$homogen

#models
summary(mod_model$model1)

## 
## Call:
## lm(formula = allformulas$eq1, data = finaldata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      39.967108   0.475057  84.131  < 2e-16 ***
## Vid_Games         0.169625   0.068473   2.477 0.013616 *  
## CaUnTs            0.760093   0.049458  15.368  < 2e-16 ***
## Vid_Games:CaUnTs  0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

#summary(mod_model$model1low)
#summary(mod_model$model1high)
mod_model$interpretation

## [1] "At low levels of CaUnTs, you see that every unit increase in Vid_Games predicts -0.09 unit change in Aggression. \n\nAt average levels of CaUnTs, you see that every unit increase in Vid_Games predicts 0.17 unit change in Aggression. \n\nAt high levels of CaUnTs, you see that every unit increase in Vid_Games predicts 0.43 unit change in Aggression."

#graphs
mod_model$graphslopes

Summary

• In this lecture, we have covered:

  • Mediation
  • Moderation
  • Special packages for these models
  • Follow ups for these models